Related papers: The graph alignment problem: fundamental limits an…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
In this paper we consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. We are given an undirected graph in which every edge is assigned a probability of existence and a positive…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Fueled by algorithmic advances, AI algorithms are increasingly being deployed in settings subject to unanticipated challenges with complex social effects. Motivated by real-world deployment of AI driven, social-network based suicide…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
Graph learning problems are typically approached by focusing on learning the topology of a single graph when signals from all nodes are available. However, many contemporary setups involve multiple related networks and, moreover, it is…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Error-tolerant graph matching gathers an important family of problems. These problems aim at finding correspondences between two graphs while integrating an error model. In the Graph Edit Distance (GED) problem, the insertion/deletion of…
We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are…